Optimal receiver antenna location in indoor environment using dynamic differential evolution and genetic algorithm

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University of Nebraska - Lincoln

DigitalCommons@University of Nebraska - Lincoln

Faculty Publications from the Department of

Electrical and Computer Engineering

Electrical & Computer Engineering, Department of

2013

Optimal receiver antenna location in indoor

environment using dynamic differential evolution

and genetic algorithm

Shu-Han Liao

Tamkang University

Chien-Hung Chen

Taipei College of Maritime Technology

Chien-Ching Chiu

Tamkang University, [email protected]

Min-Hui Ho

Tamkang University

Tadeusz A. Wysocki

University of Nebraska-Lincoln

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Liao, Shu-Han; Chen, Chien-Hung; Chiu, Chien-Ching; Ho, Min-Hui; Wysocki, Tadeusz A.; and Wysocki, Beata J., "Optimal receiver antenna location in indoor environment using dynamic differential evolution and genetic algorithm" (2013). Faculty Publications from

the Department of Electrical and Computer Engineering. 388. http://digitalcommons.unl.edu/electricalengineeringfacpub/388

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Authors

Shu-Han Liao, Chien-Hung Chen, Chien-Ching Chiu, Min-Hui Ho, Tadeusz A. Wysocki, and Beata J.

Wysocki

This article is available at DigitalCommons@University of Nebraska - Lincoln:http://digitalcommons.unl.edu/ electricalengineeringfacpub/388

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R E S E A R C H

Open Access

Optimal receiver antenna location in indoor

environment using dynamic differential evolution

and genetic algorithm

Shu-Han Liao

1

, Chien-Hung Chen

2

, Chien-Ching Chiu

1*

, Min-Hui Ho

1

, Tadeusz A Wysocki

3

and Beata J Wysocki

3

Abstract

Using the impulse responses of these multipath channels, the bit error rate (BER) performance for binary pulse amplitude modulation impulse radio ultra-wideband communication system is calculated. The optimization location of receiving antenna is investigated by dynamic differential evolution (DDE) and genetic algorithm (GA) to minimize the outage probability. Numerical results show that the performance for reducing BER and outage probability by DDE algorithm is better than that by GA.

Keywords: BER; BPAM; UWB; DDE; GA 1 Introduction

Ultra-wideband (UWB) transmissions can legally operate in the range from 3.1 up to 10.6 GHz at a limited transmit power of−41 dBm/MHz [1]. All wireless systems must be able to deal with the challenges of operating over a multipath propagation channel, where the object in the environment can cause multiple reflections. Bit error rate (BER) degradation is caused by the inter-symbol interfer-ence due to a multipath propagation made up of radio wave reflections by walls, ceilings, floors, and office fix-tures. In general, effective antenna selection and deploy-ment strategies are important for reducing BER in indoor wireless systems [2,3]. To the best of our knowledge, there is still no investigation using the dynamic differential evo-lution (DDE) and genetic algorithm (GA) to optimize the location of receiving antennas for minimizing the BER in indoor wireless communication channel.

Based on the BER formula, the outage probability is chosen as the cost function in our optimization procedure. Thus, the optimization of location of receiving antenna in this paper is using DDE and GA to overcome the above situation and to minimize the outage probability.

The remainder of this paper is organized as follows: In Section 2, channel modeling, system description, dynamic

differential evolution, and genetic algorithm procedure are presented. The numerical results are then presented in Section 3, and conclusion is made in Section 4.

2 Channel modeling and system description

2.1 Channel modeling

The following two steps are used to calculate the multipath radio channel:

1. Frequency responses for sinusoidal waves by shooting and bouncing ray (SBR)/image[4-23] techniques. The SBR/image method can deal with high-frequency radio wave propagations in the complex indoor environments [24,25].

2. Inverse fast Fourier transform (IFFT) and Hermitian processing. The frequency responses are transformed to the time domain using the inverse Fourier transform with the Hermitian signal processing [26]. Using the Hermitian processing, the pass-band signal is obtained with zero padding from the lowest frequency down to direct current (DC), taking the conjugate of the signal and reflecting it to the negative frequencies. The result is then transformed to the time domain using IFFT [27]. Since the signal spectrum is symmetric around DC. The resulting doubled-side spectrum corresponds to a real signal in the time domain.

* Correspondence:[email protected]

1

Department of Electrical Engineering, Tamkang University, Tamsui District, New Taipei City 251, Taiwan

Full list of author information is available at the end of the article

© 2013 Liao et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Liao et al. EURASIP Journal on Wireless Communications and Networking 2013, 2013:235 http://jwcn.eurasipjournals.com/content/2013/1/235

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The equation for modeling the multipath radio chan-nel is a linear filter with an impulse response given by

h tð Þ ¼X N n¼1

αnδ t−τð nÞ; ð1Þ

where N is the number of paths observed at time, δ(·) is the Dirac delta function, and anand τn are the channel gain and time delay for the n-th path, respectively.

2.2 System block diagram

The block diagram of the simulated communication sys-tem is shown in Figure 1. The received signal r(t) can be expressed as follows:

r tð Þ ¼ x t½ ð Þ⊗h tð Þ þ n tð Þ; ð2Þ where x(t) is the transmitted signal, h(t) is the impulse response of the equivalent baseband, and n(t) is the white Gaussian noise with zero mean and variance N0/2.

The transmitted UWB pulse stream can be expressed as follows [28]:

x tð Þ ¼X ∞ n¼1

p t− n−1½ ð ÞTddn; ð3Þ

where p(t) is the transmitted waveform. dn ∊ {±1} is a binary pulse amplitude modulation (B-PAM) symbol and is assumed to be independent and identically distributed. Td is the duration of the transmitting signal. The trans-mitted waveform p(t) is the Gaussian waveform with ultra-short duration Tp at the nanosecond scale. Note that Tdis the duration of the transmitting signal, and Tp is the pulse duration. The value of Td is usually much larger than that of Tp. The Gaussian waveform p(t) can be described by the following expression:

p tð Þ ¼ ffiffiffiffiffiffi1 2π p σe −t2 2σ2 ; ð4Þ

where t and σ are time and standard deviation of the Gaussian wave, respectively. The average transmit energy symbol Etcan be expressed as

Et ¼

∫

Td 0 p 2 t ð Þdt; ð5Þ

where Etis the average transmitted energy.

The correlation receiver samples the received signal at the symbol rate and correlates them with suitably de-layed references given by

q tð Þ ¼ p t−τ½ 1− n−1ð ÞTd; ð6Þ

whereτ1is the delay time of the first wave. The output of the correlator at t = nTdis [29,30]: Z nð Þ ¼ ∫ nTd n−1 ð ÞTd X∞ n¼1 p t− n−1½ ð ÞTddn " # ⊗h tð Þ ( ) ⋅q tð Þdt þ ∫nTd n−1 ð ÞTdn tð Þq tð Þdt ¼ V nð Þ þ η nð Þ: ð7Þ

It can be shown that the noise components η(n) of Equation 7 are uncorrelated Gaussian random variables with zero mean. The variance of the output noiseη is

σ2_{¼ N}0

2 Et: ð8Þ

The conditional error probability of the n-th bit is thus expressed by Pe Z nð Þ ⇀d ¼1 2erfc V nð Þ_ffiffiffi 2 p σ ⋅ dð Þn ; ð9Þ where erfc xð Þ ¼p2ffiffiffi_π_∫∞ xe−y 2 dy is complementary error function and ⇀d n o

¼ df 0; d1; …; dng is the binary se-quence. Note that the average BER for B-PAM impulse radio UWB system can be expressed as [10]

BER¼X 2n i¼1 P ⇀d ⋅1 2erfc V ið Þ_ffiffiffi 2 p σ⋅ dð Þn ; ð10Þ where P ⇀d

is the occurring probability of the binary sequence⇀d.

2.3 Dynamic differential evolution

In dynamic differential evolution (DDE), after generating the initial population, the candidate solutions are refined by applying mutation, crossover, and selection, itera-tively. The flowchart of the DDE algorithm is shown in Figure 2. In this strategy, a mutant vector for each target vector Vkþ1_j at the k + 1 generation is computed by

Vkþ1_j i ¼ Xk j i þ ζ⋅ Xk best i− Xk j i h i þ χ⋅ Xk m i− Xk n i ; j; m; n∈ 0; Np−1 ; m≠n; ð11Þ where i = 1 ~ D and χ and ζ are the scaling factors asso-ciated with the vector differences Xk_best−Xk_j

and Xk

m−Xkn

, respectively. The disturbance vector V due to the mutation mechanism consists of parameter vector Xk_j, the best particle Xk

best, and two randomly selected vectors. As comparison, the mutant vector Vkþ1_j is generated according to Equation 12 for typical DE [31]:

Liao et al. EURASIP Journal on Wireless Communications and Networking 2013, 2013:235 Page 2 of 9

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Vkþ1_j i ¼ Xkj i þ χ⋅ Xkm i− Xkn i ; j; m; n ∈ 0; Np−1 ; m≠n; ð12Þ

where i = 1 ~ D and χ is the scaling factor associated with the vector difference X k_m−Xk_n . Note thatζ is set to 0 for DE; therefore, the main differences between DDE and DE is that DDE includes the idea of approaching the‘best’ dur-ing the course of optimization procedure.

After mutation, the crossover operator is applied to generate another kind of new vector uj. The crossover operation in DDE delivers the crossover vector ukþ1

j by

mixing the components of the current vector Xiand the above mutant vector Vi. It can be expressed as

ukþ1_j ¼ Vkþ1 j i;Qk< CR Xk j i;Qk≥ CR; 8 < : ð13Þ where i = 1 ~ D and Qkis a random number uniformly distributed within [0,1]. CR∊ (0, 1) is a predefined cross-over rate. DDE uses a greedy selection operator that is defined by Xkþ1_j ¼ u kþ1 j ; if CF ukj < CF Xk j Xk j; otherwise: ( ð14Þ Selection operation is conducted by comparing the parent vector Xkþ1_j with the crossover vector ukþ1_j . The vector with smaller cost function (CF) value is selected as a member for the next generation.

In the synthesis procedure, the DDE is used to minimize the following CF:

CF¼ outage probability; ð15Þ

where cost function is the outage probability for UWB system. The outage probabilities for 100-Mbps B-PAM and for a BER < 10−3versus SNR are calculated. DDE is used to search the receiver antenna location to minimize the outage probability of the communication system. This SBR/image method technique is used to calculate the UWB channel impulse response for each location of the receiver. Based on the channel impulse response, the number of multipath components, the root mean square (RMS) delay spread τRMS, and the mean excess delay τMEDare computed. The DDE algorithm iteratively gen-erates a new population that springs from the previous population through the application of the reproduction by mutation and replacement operators. In our simula-tion, when the cost function is bigger than the threshold Figure 1 Block diagram of the simulated communication

system.

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value or DDE does not find a better individual within 300 successive generations, the DDE will be terminated, and a solution is then obtained.

2.4 Genetic algorithm

Genetic algorithm (GA) is the global numerical optimization methods based on genetic recombination and evaluation in

nature [32,33]. They use the iterative optimization proce-dures, which start with a randomly selected population of potential solutions and then gradually evolve toward a better solution through the application of the genetic operators. GA typically operates on a discretized and coded representa-tion of the parameters rather than on the parameters them-selves. These representations are often considered to be Figure 2 The flowchart of the dynamic differential evolution.

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‘chromosomes’, while the individual element, which con-stitutes chromosomes, is the‘gene’ . Simple but often very effective chromosome representations for optimization problem involving several continuous parameters can be obtained through the juxtaposition of discretized binary representations of the individual parameter.

We regulate the receiver antenna location of the indoor environment to minimize the outage probability. The GA starts with a population containing a total of GPcandidates (i.e., GPis the population size). Each candidate is described by a chromosome. Then, the initial population can simply be created by taking GPrandom chromosomes. GA itera-tively generates a new population, which is derived from the previous population through the application of the reproduction, crossover, and mutation operators.

The GA is used to minimize the cost function in Equation 15, where cost function is the outage probabil-ity for UWB system. Through repeated applications of reproduction, crossover, and mutation operators, the ini-tial population is transformed into a new population in an iterative manner. New populations will contain in-creasingly better chromosomes and will eventually con-verge to an optimal population that consists of the optimal chromosomes.

As for the GA calculations, each chromosome is assigned information of the position of transmitter as the optimization variables. For each generated chromosome, the GA reruns the ray tracing program to calculate the BER for each receiver from the given location of transmit-ter provided by the chromosome. In our simulation, when the BER is lower than the threshold value or GA does not find a better individual within 300 successive generations, the GA will be terminated and a solution is then obtained.

3 Numerical results

A ray tracing technique is developed to calculate the channel impulse response from 3.1 to 10.6 GHz with frequency interval of 5 MHz, i.e., 1,501 frequency compo-nents are used. Since the dielectric constant and conduct-ivity of the materials change with frequency, the different values of dielectric constant and conductivity of materials for different frequencies are carefully considered in chan-nel calculation [34-37]. The BER for different receiver positions in the indoor environments are investigated. Figure 3 is the top view of the indoor environment with dimensions of 10 m (length) × 9.2 m (width) × 3 m (height). The transmitting and receiving antennas are with simple omnidirectional radiation pattern and vertically

Figure 3 A plan view of the simulated environment.

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Figure 5 Optimized receiver position when only one receiver is used. (▼) Receiver position RxCenteris located in the center of the indoor

environment. (▲) GA optimized receiver position RxGA. (■) DDE optimized receiver position RxDDE.

Figure 4 Outage areas (BER > 10−3) with the use of one transmitter.

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polarized. Each antenna is with a fixed height of 1 m. The optimal antenna location for minimizing the outage prob-ability is searched by DDE and GA. The relative coeffi-cients of the DDE are set as follows: The scaling factors of F and λ are both 0.8, and the crossover rate CR = 0.6. The population size Np= 30. The relative coefficients of the GA are set as follows: The crossover rate Gr= 0.6. The mutation probability GM = 0.025, and the population size GP = 30. The cases with different transceiver positions are considered in our simulation. The receiving antenna RxCenter(5 m × 4.6 m × 0.73 m) located in the center of the indoor environment with a fixed height of 1 m is used for our ref-erence, as shown in Figure 3.

Based on the channel impulse response, the number of multipath components, the RMS delay spreadτRMS, and the mean excess delayτMEDare computed. The cu-mulative distributions of the RMS delay spread τRMSis defined as [38] τRMS¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XN n¼1 τn2j jan2 G − XN n¼1 τnj jan2 G 0 B B B B @ 1 C C C C A 2 v u u u u u u u t ; ð16Þ where G ¼X N n¼1 an j j2

is the total multipath gain. The mean excess delay,τMED, is defined as [39]

τMED¼ XN n¼1

τnj jan2

G : ð17Þ

By Equations 16 and 17, we can obtain the RMS delay spreads and mean excess delay.

We compare the effects of RxCenter, RxDDE, and RxGAon UWB transmission. For the case, the receiver is mobile in the whole indoor environment and the transceivers are lo-cated on the desk, in which 25 measurements are carried out (e.g., transmission from a computer ‘Tx’ to a printer ‘Rx’). Figure 4 shows that the transmitting antenna RxCenter(5 m × 4.6 m × 0.73 m) is located in the center of the indoor environment. In this case, six bad receiving signal points (BER > 10−3) occurred including (not high-lighted in the figure) the transmitter points. The DDE and GA optimization position of the receiver is shown in Figure 5. The optimal locations of the receiving anten-nas are at RxDDE (3.52 m × 6.25 m × 0.73 m) and RxGA (3.56 m × 6.24 m × 0.73 m) using the DDE and GA, re-spectively. The optimization receiver points RxDDE and RxGA are chosen as the receiver locations as squares/tri-angle, and no bad transmitting signal point exists. The out-age probability versus SNR is calculated, as shown in Figure 6. Here, SNR is defined as the ratio of the average transmitted power to the noise power at the front end of the receiver. It is seen that the outage probability at SNR = 28 dB are about 68%, 8%, and 12% for RxCenter, RxDDE, and RxGA, respectively. It is clear that the outage probability decreased by DDE is better than those by GA about 50%. The performance for the antenna location by DDE is better than that by GA.

Table 1 The channel parameters (τMEDandτRMS) for the two kinds of algorithms

Transmitter channel parameters

τMED(ns) τRMS(ns) RxCenter 7.64 12.50 RxGA 2.86 7.12 RxDDE 2.80 6.69

0

100

200

300

400

500

0

10

20

30

40 Generation

Out

age Probabilit

y

(%)

Rx

GA

Rx

DDE

Figure 7 Average outage probability versus generations by two different algorithms.

0

5 10 15 20 25 30 35 40

0

20

40

60

80

100 SNR

t

(dB)

Out

age Probabilit

y

(%)

Rx

Center

Rx

GA

Rx

DDE

Figure 6 Outage probability versus SNR for the two kinds of algorithms.

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The outage probability versus generation DDE and GA are calculated, as shown in Figure 7. It is found that the outage probability decreases quickly by the DDE, and good convergences are achieved within 182 generations. It also shows that the convergent speed for the DDE is faster than that for GA.

In order to determine the multipath effect, the τRMS and τMED were calculated. A summary of these values are given in Table 1 for scenarios. For the transceivers lo-cated on the table's case scenario, the τRMS for RxCenter, RxDDE, and RxGAare 12.5, 2.80, and 2.86 ns, respectively. It is clear that theτRMSfor the RxCentercase is the biggest.

4 Conclusions

Using the impulse responses of these multipath channels, the BER performance for UWB communication system is calculated. The DDE and GA are used to minimize the BER. Numerical results show that BER in the cases can be de-creased. It is also found that the BER decreased by DDE is better than that by GA. Numerical results also show that the DDE outperforms the GA in convergence speed. Competing interests

The authors declare that they have no competing interests. Author details

1_{Department of Electrical Engineering, Tamkang University, Tamsui District,}

New Taipei City 251, Taiwan.2Department of Computer and Communication

Engineering, Taipei College of Maritime Technology, Danshui Town, New

Taipei City 251, Taiwan.3Peter Kiewit Institute, University of Nebraska-Lincoln,

Lincoln, NE 68588, USA.

Received: 8 May 2013 Accepted: 3 September 2013 Published: 25 September 2013

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doi:10.1186/1687-1499-2013-235

Cite this article as: Liao et al.: Optimal receiver antenna location in indoor environment using dynamic differential evolution and genetic algorithm. EURASIP Journal on Wireless Communications and Networking 2013 2013:235.

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